Shaomin Wu

Linear and Nonlinear Preventive Maintenance Models

Preventive maintenance (PM) is a maintenance program with activities initiated at predetermined intervals, or according to prescribed criteria, and intended to reduce the probability of failure, or the degradation of the functioning of an item. In the literature, a number of PM models have been introduced to depict the effectiveness of PM. Based on these models, approaches to scheduling PM policies have been considerably studied. This paper attempts to review existing PM models, and investigate their inter-relationships. We then categorize these models into three classes: linear, nonlinear, and a hybrid of both. These three PM model classes depict the relationships of the hazard functions before, and after a PM. Possible extensions to these three PM models are discussed. The statistical properties for models are derived, and approaches to optimizing the PM policy are given.

Optimal maintenance policies under different operational schedules

In the reliability literature, maintenance time is usually ignored during the optimization of maintenance policies. In some scenarios, costs due to system failures may vary with time, and the ignorance of maintenance time will lead to unrealistic results. This paper develops maintenance policies for such situations where the system under study operates iteratively at two successive states: up or down. The costs due to system failure at the up state consist of both business losses & maintenance costs, whereas those at the down state only include maintenance costs. We consider three models: Model A, B, and C: /spl middot/ Model A makes only corrective maintenance (CM). /spl middot/ Model B performs imperfect preventive maintenance (PM) sequentially, and CM. /spl middot/ Model C executes PM periodically, and CM; this PM can restore the system as good as the state just after the latest CM. The CM in this paper is imperfect repair. Finally, the impact of these maintenance policies is illustrated through numerical examples.

Preventive maintenance models with random maintenance quality

In real-world environments it is usually difficult to specify the quality of a preventive maintenance (PM) action precisely. This uncertainty makes it problematic to optimise maintenance policy. This problem is tackled in this paper by assuming that the quality of a PM action is a random variable following a probability distribution. Two frequently studied PM models, a failure rate PM model and an age reduction PM model, are investigated. The optimal PM policies are presented and optimised. Numerical examples are also given.

A review on coarse warranty data and analysis

Abstract Warranty data contain useful information about product quality and reliability, but they are usually coarse data because they may be aggregated, delayed, censored, missing or vague. They might, however, be the only forms of warranty data a manufacturer has, analysing such data are therefore needed and can also be of benefit to manufacturers in identifying early warnings of abnormalities in their products, providing useful information about failure modes to aid design modification, estimating product reliability for deciding on warranty policy, and forecasting future warranty claims needed for preparing warranty reserves plans. In last two decades, considerable research has been conducted in analysing coarse warranty data (CWD) from several different perspectives. This paper categorises different types of CWD and reviews techniques to analyse such data. It concludes with research needs in CWD.

Performance utility-analysis of multi-state systems

This paper defines a new utility importance of a state of a component in multi-state systems. This utility importance overcomes some drawbacks of a well-known importance measure suggested by William S. Griffith (J. Applied Probability, 1980). The relationship between this new utility importance and the Griffith importance is studied and their difference is illustrated with examples. The contribution of an individual component to the performance utility of a multi-state system is discussed. Examples show that a meaningful index for measuring the performance of individual components in a multi-state system can hardly be defined in general, without considering the actual values of the utility levels and the distributions of the component-states in the system. An example illustrates how genetic algorithm, simulated annealing, and tabu search can be used in selecting components and defining the position order of components so that the performance utility of a multi-state system is optimized.

Joint importance of multistate systems

Importance measures in reliability engineering are used to identify weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system. Traditional importance measures for multistate systems mainly concern reliability importance of an individual component and seldom consider the utility performance of the systems. This paper extends the joint importance concepts of two components from the binary system case to the multistate system case. A joint structural importance and a joint reliability importance are defined on the basis of the performance utility of the system. The joint structural importance measures the relationship of two components when the reliabilities of components are not available. The joint reliability importance is inferred when the reliabilities of the components are given. The properties of the importance measures are also investigated. A case study for an offshore electrical power generation system is given.

Optimizing replacement policy for a cold-standby system with waiting repair times

This paper presents the formulas of the expected long-run cost per unit time for a cold-standby system composed of two identical components with perfect switching. When a component fails, a repairman will be called in to bring the component back to a certain working state. The time to repair is composed of two different time periods: waiting time and real repair time. The waiting time starts from the failure of a component to the start of repair, and the real repair time is the time between the start to repair and the completion of the repair. We also assume that the time to repair can either include only real repair time with a probability p, or include both waiting and real repair times with a probability 1-p. Special cases are discussed when both working times and real repair times are assumed to be geometric processes, and the waiting time is assumed to be a renewal process. The expected long-run cost per unit time is derived and a numerical example is given to demonstrate the usefulness of the derived expression.

Construction of Asymmetric Copulas and Its Application in Two-Dimensional Reliability Modelling

Copulas offer a useful tool in modelling the dependence among random variables. In the literature, most of the existing copulas are symmetric while data collected from the real world may exhibit asymmetric nature. This necessitates developing asymmetric copulas that can model such data. In the meantime, existing methods of modelling two-dimensional reliability data are not able to capture the tail dependence that exists between the pair of age and usage, which are the two dimensions designated to describe product life. This paper proposes a new method of constructing asymmetric copulas, discusses the properties of the new copulas, and applies the method to fit two-dimensional reliability data that are collected from the real world.

Warranty claim analysis considering human factors

Abstract Warranty claims are not always due to product failures. They can also be caused by two types of human factors. On the one hand, consumers might claim warranty due to misuse and/or failures caused by various human factors. Such claims might account for more than 10% of all reported claims. On the other hand, consumers might not be bothered to claim warranty for failed items that are still under warranty, or they may claim warranty after they have experienced several intermittent failures. These two types of human factors can affect warranty claim costs. However, research in this area has received rather little attention. In this paper, we propose three models to estimate the expected warranty cost when the two types of human factors are included. We consider two types of failures: intermittent and fatal failures, which might result in different claim patterns. Consumers might report claims after a fatal failure has occurred, and upon intermittent failures they might report claims after a number of failures have occurred. Numerical examples are given to validate the results derived.

Reliability analysis of two-unit cold standby repairable systems under Poisson shocks

Abstract This paper analyses the reliability of a cold standby system consisting of two repairable units, a switch and a repairman. At any time, one of the two units is operating while the other is on cold standby. The repairman may not always at the job site, or take vacation. We assume that shocks can attack the operating unit. The arrival times of the shocks follow a homogeneous Poisson process and their magnitude is a random variable following a known distribution. Time on repairing a failed unit and the length of repairman’s vacation follow general continuous probability distributions, respectively. The paper derives a number of reliability indices: system reliability, mean time to first failure, steady-state availability, and steady-state failure frequency.